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We introduce the game-theoretic stochastic routing (GTSR) framework, a proactive alternative to today's reactive approaches to route repair. GTSR minimizes the impact of link and router failure by 1) computing multiple paths between source and destination and 2) selecting among these paths randomly to forward packets. Besides improving fault tolerance, the fact that GTSR makes packets take random paths from source to destination also improves security. In particular, it makes connection eavesdropping attacks maximally difficult as the attacker would have to listen on all possible routes. The approaches developed are suitable for network layer routing, as well as for application layer overlay routing and multipath transport protocols such as the stream control transmission protocol (SCTP). Through simulations, we validate our theoretical results and show how the resulting routing algorithms perform in terms of the security/fault-tolerant/delay/throughput trade-off. We also show that a beneficial side effect of these algorithms is an increase in throughput, as they make use of multiple paths.